Underwater Robots - Gianluca Antonelli.pdf

9.2 Kinematic Control of AUVs 227
communication constraint istaken into account also in[188] with numerical
simulations of the effects of communication delays on the formation.
Reference [64] reports the development ofanadaptive on-line planning
algorithm for the exploration of an unknown oceanic environment bymeans
of several AUVs. The aim is to have amap of the estimation ofadesired
variable such as, e.g., the water temperature, in aregion. Each vehicle decides
the next measurements on the basis of the current measurement and the
past measurements of all the platoon such that the confidence level of the
overall estimation is locally increased. The paper reports simulation results,
an experimental set-up is currently under development based onself-designed
low-cost vehicles [6, 7].
In [136] aLypanuov-based technique is derived so that the underwater
vehicles, supposedfullyactuated, are steered along aset of spatial paths while
keeping agiven inter-vehicle formation. The path following for each vehicle is
essentially decoupled while its advancing velocity isproperly shaped sothat
the formation is properly achieved. Simulation results on aplanar formation
of 3vehicles are provided.
In the following Section aspecific control strategy, based oninverse kinematics
algorithms for fixed-base manipulators, is discussed together with
some simulation results; finally, the description of the experimental set-up of
the Virginia Polytechnic Institute &State University isprovided.
9.2 Kinematic Control of AUVs
In 2001 [48, 50, 277] B.E. Bishop and D.J. Stilwell for the first time recognize
aformal similarity between the problem of robot redundancy resolution and
the achievement ofplatoon’s tasks at the differential level. The primary task
is defined by the platoon’s mean and variance and tasks such asobstacle
avoidance and heading control are handled assecondary tasks by using the
approach developed by Y. Nakamura [210]. G. Antonelli and S.Chiaverini,
in [27, 28, 30], inherited this approach byproposing adifferent way to handle
the redundancy with respect to the given task, specifically, the task priority
redundancy resolution proposed by S. Chiaverini [78].
Task Functions and Inverse Kinematics
While considering aplatoon of n vehicles, the aim is to control thevaluetaken
by ageneric task function which suitably depends on the platoon state; an
example of such function isthe one expressing the mean value of all the
vehicles’ positions as asynthetic data about the platoon location.
3 n
To keep the notation compact it is useful to define the vector p ∈ IR
p =
⎡
⎢
⎣
η 1 , 1
.
.
η 1 ,n
⎤
⎥
⎦